展開する (b/a (x-x_{0})+y_{0}-c)^2

解

展開する

(\frac{b}{a} (x - x_{0}) + y_{0} - c)^{2}

\frac{b ^{2} ( x - x _{0} ) ( x - x _{0} )}{a ^{2}} + \frac{2 b x y _{0} - 2 b x _{0} y _{0} - 2 b c x + 2 b c x _{0}}{a} + y_{0}^{2} - 2 c y_{0} + c^{2}

解答ステップ

(\frac{b}{a} (x - x_{0}) + y_{0} - c)^{2}

指数の規則を適用する:

a^{b + c} = a^{b} \cdot a^{c}

(\frac{b}{a} (x - x_{0}) + y_{0} - c)^{2} = (\frac{b}{a} (x - x_{0}) + y_{0} - c) (\frac{b}{a} (x - x_{0}) + y_{0} - c)

= (\frac{b}{a} (x - x_{0}) + y_{0} - c) (\frac{b}{a} (x - x_{0}) + y_{0} - c)

括弧を分配する

= \frac{b}{a} (x - x_{0}) \frac{b}{a} (x - x_{0}) + \frac{b}{a} (x - x_{0}) y_{0} + \frac{b}{a} (x - x_{0}) (- c) + y_{0} \frac{b}{a} (x - x_{0}) + y_{0} y_{0} + y_{0} (- c) - c \frac{b}{a} (x - x_{0}) - c y_{0} - c (- c)

簡素化

\frac{b}{a} (x - x_{0}) \frac{b}{a} (x - x_{0}) + \frac{b}{a} (x - x_{0}) y_{0} + \frac{b}{a} (x - x_{0}) (- c) + y_{0} \frac{b}{a} (x - x_{0}) + y_{0} y_{0} + y_{0} (- c) - c \frac{b}{a} (x - x_{0}) - c y_{0} - c (- c) : \frac{b ^{2} ( x - x _{0} ) ( x - x _{0} )}{a ^{2}} + \frac{2 b x y _{0} - 2 b x _{0} y _{0} - 2 b c x + 2 b c x _{0}}{a} + y_{0}^{2} - 2 c y_{0} + c^{2}

= \frac{b ^{2} ( x - x _{0} ) ( x - x _{0} )}{a ^{2}} + \frac{2 b x y _{0} - 2 b x _{0} y _{0} - 2 b c x + 2 b c x _{0}}{a} + y_{0}^{2} - 2 c y_{0} + c^{2}